A Structural Approach to the Design of Domain Specific Neural Network Architectures

TL;DR

This thesis explores the theoretical foundations of geometric deep learning, focusing on how neural network architectures can be designed to be invariant or equivariant to data transformations, aiming to improve understanding and performance.

Contribution

It provides a theoretical evaluation of invariant neural networks, compiling key results that characterize their properties and influence on learning performance.

Findings

Theoretical characterization of invariant neural networks

Analysis of invariance and equivariance in geometric deep learning

Insights into how invariance affects learning performance

Abstract

This is a master's thesis concerning the theoretical ideas of geometric deep learning. Geometric deep learning aims to provide a structured characterization of neural network architectures, specifically focused on the ideas of invariance and equivariance of data with respect to given transformations. This thesis aims to provide a theoretical evaluation of geometric deep learning, compiling theoretical results that characterize the properties of invariant neural networks with respect to learning performance.